cp's OEIS Frontend

A355146 Triangle read by rows: T(n,k) is the number of subsets of {1,...,n} of cardinality k in which every pair of elements is coprime; n >= 0, 0 <= k <= A036234(n).

%I A355146 #16 Jul 06 2022 17:42:50
%S A355146 1,1,1,1,2,1,1,3,3,1,1,4,5,2,1,5,9,7,2,1,6,11,8,2,1,7,17,19,10,2,1,8,
%T A355146 21,25,14,3,1,9,27,37,24,6,1,10,31,42,26,6,1,11,41,73,68,32,6,1,12,45,
%U A355146 79,72,33,6,1,13,57,124,151,105,39,6,1,14,63,138,167,114,41,6
%N A355146 Triangle read by rows: T(n,k) is the number of subsets of {1,...,n} of cardinality k in which every pair of elements is coprime; n >= 0, 0 <= k <= A036234(n).
%C A355146 For n >= 1, the alternating row sums equal 0.
%H A355146 Marcel K. Goh and Jonah Saks, <a href="https://arxiv.org/abs/2206.12535">Alternating-sum statistics for certain sets of integers</a>, arXiv:2206.12535 [math.CO], 2022.
%e A355146 Triangle T(n,k) begins:
%e A355146   n/k 0  1  2  3  4  5 6
%e A355146   0   1
%e A355146   1   1  1
%e A355146   2   1  2  1
%e A355146   3   1  3  3  1
%e A355146   4   1  4  5  2
%e A355146   5   1  5  9  7  2
%e A355146   6   1  6 11  8  2
%e A355146   7   1  7 17 19 10  2
%e A355146   8   1  8 21 25 14  3
%e A355146   9   1  9 27 37 24  6
%e A355146   10  1 10 31 42 26  6
%e A355146   11  1 11 41 73 68 32 6
%e A355146   12  1 12 45 79 72 33 6
%e A355146   ...
%e A355146 For n=8 and k=5 the T(8,5)=3 sets are {1,2,3,5,7}, {1,3,4,5,7}, and {1,3,5,7,8}.
%Y A355146 Row sums give A084422.
%Y A355146 Cf. A000720, A036234, A186974, A320436.
%K A355146 nonn,tabf
%O A355146 0,5
%A A355146 _Marcel K. Goh_, Jun 27 2022